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arXiv:2403.17941 · Entropy

Entanglement of Temporal Sections as Quantum Histories and Their Quantum Correlation Bounds

Marcin L Nowakowski

Published Feb 26, 2024• 2 citations
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Abstract

In this paper, we focus on the underlying quantum structure of temporal correlations and show their peculiar nature which differentiates them from spatial quantum correlations. With a growing interest in the representation of quantum states as topological objects, we consider quantum history bundles based on the temporal manifold and show the source of the violation of monogamous temporal Bell-like inequalities. We introduce definitions for the mixture of quantum histories and consider their entanglement as sections over the Hilbert vector bundles. As a generalization of temporal Bell-like inequalities, we derive the quantum bound for multi-time Bell-like inequalities.

DOI
10.3390/e26030198

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In this paper, we focus on the underlying quantum structure of temporal correlations and show their peculiar nature which differentiates them from spatial quantum correlations. With a growing interest in the representation of quantum states as topological objects, we consider quantum history bundles based on the temporal manifold and show the source of the violation of monogamous temporal Bell-like inequalities. We introduce definitions for the mixture of quantum histories and consider their entanglement as sections over the Hilbert vector bundles. As a generalization of temporal Bell-like inequalities, we derive the quantum bound for multi-time Bell-like inequalities.
In this paper we focus on the underlying quantum structure of temporal correlations and show their peculiar nature which differentiate them from spatial quantum correlations. We show rigorously that a particular entangled history, which can be associated with a quantum propagator, is monogamous to conserve its consistency throughout time. Yet evolving systems violate monogamous Bell-like multi-time inequalities. This dichotomy, being a novel feature of temporal correlations, has its roots in the measurement process itself which is discussed by means of the bundles of entangled histories. We introduce and discuss a concept of a probabilistic mixture of quantum processes by means of which we clarify why the spatial-like Bell-type monogamous inequalities are further violated. We prove that Tsirelson bound on temporal Bell-like inequalities can be derived from the entangled histories approach and as a generalization, we derive the quantum bound for multi-time Bell-like inequalities. It is also pointed out that what mimics violation of monogamy of temporal entanglement is actually just a kind of polyamory in time but monogamy of entanglement for a particular evolution still holds.
In this paper we state a fundamental question about the structure of correlations in time and analyze temporal monogamy relations. We show that the nature of temporal correlations is inherently different from the spatial ones but in similarity to quantum spatial correlations, we expose a phenomenon of monogamy of quantum entanglement in time. We perform this task applying the entangled histories framework as a modifcation of the consistent histories approach. These considerations are supported by introduction of necessary tools specific for the tensor algebra used for representation of spatial correlations. We show that Tsirelson bound on temporal Bell-like inequalities can be derived from the entangled histories approach. Finally, we point out that in a context of the tensor algebra used for linking states in different times further studies on mathematical structure of the state representing evolving systems are needed.
Abstract Multipartite quantum correlations are a powerful resource that underpins applications from quantum metrology to quantum computing. While most research has focused on spatial correlations, it is now becoming clear that a sequence of measurements on a single quantum system at different points in time reveals a similarly rich, yet fundamentally different structure of multipartite temporal correlations. Here we experimentally observe genuine multi-time correlations in a sequence of three generalized measurements on a single photon. These correlations, manifest by a simultaneous violation of all pairwise Bell inequalities, cannot be reproduced by any spatial quantum state of equal dimension. Our work lays the foundation for the exploration of temporal correlations arising in quantum networks for quantum information applications.
Abstract The formalism of generalized quantum histories allows a symmetrical treatment of space and time correlations, by taking different traces of the same history density matrix. In this framework, the characterization of spatial and temporal entanglement is revisited. An operative protocol is presented, to map a history state into the ket of a static composite system. It is demonstrated, by examples, how the Leggett–Garg and the temporal Clauser‐Horne‐Shimony‐Holt (CHSH) inequalities can be violated in this approach.
We present a reformulation of quantum entanglement and Bell-type correlations based on a dynamically emergent temporal structure defined by a future-directed vector field Φμ(x)\Phi^\mu(x)Φμ(x). This intrinsic temporal flow induces a physical foliation of spacetime, enabling a causal, local, and covariant account of quantum correlations. Within this framework, entangled states are described as topologically and causally coherent field configurations, and Bell inequality violations arise without requiring acausal nonlocality. Our results suggest a new geometric foundation for quantum nonlocality rooted in the spontaneous symmetry breaking of temporal order.
In this paper we present a concept of quantum entanglement in time in a context of entangled consistent histories. These considerations are supported by presentation of necessary tools closely related to those acting on a space of spatial multipartite quantum states. We show that in similarity to monogamy of quantum entanglement in space, quantum entanglement in time is also endowed with this property for a particular history. Basing on these observations, we discuss further bounding of temporal correlations and derive analytically the Tsirelson bound implied by entangled histories for the Leggett-Garg inequalities.